By Deepak Chopra, MD and Menas Kafatos, PhD
Infinity has been getting a bad reputation recently. It has become the sticking point in the story we tell ourselves about reality. The trouble begins with a split between what is real and what is unreal. If you send someone to the store to buy three apples, and they return with only one, it matches reality to say, “you only brought me a third of what I wanted.” This statement matches the way numbers are meant to behave. Numbers are pure in the sense that they are abstractions, ever-existing and perfect as the ancient Greek philosophers thought. They cannot be disturbed by real-world events. Yet they are reliable because they allow us to engineer the real world, from building bridges and cathedrals to manufacturing microchips. They are rational because they strictly obey mathematical order and perfect logic.
These three virtues are wobbly when it comes to infinity, however. Getting one apple instead of three represents a one-third return, and when written in decimals, one-third is .33333 out to infinity. In other words, it is an endless number, and “endless” isn’t something we can actually conceive. There is a mismatch between the real world and mathematics, and when it comes to advanced mathematics, the kind applied by physicists and cosmologists, the misbehavior of infinity becomes serious. (Actually, this is one kind of well-behaved infinity, because rational numbers like 1/3 can be known to any order and predicted in advance—the repetition of three continues ad infinitum. An irrational number like pi (π) is a different kind of infinity, since its digits are unpredictable and do not repeat.)
The noted physicist Max Tegmark wrote an article for Discover magazine in Feb. 2015 titled, “Infinity Is a Beautiful Concept – And It’s Ruining Physics.” The ruination exists on two disturbing fronts. The first front is theoretical. Physicists need valid, provable theories to explain the biggest and smallest things in nature. As it turns out, the smallest things, subatomic particles, wink out of sight and vanish into the quantum vacuum. The biggest things, including galactic and intergalactic matter and the universes itself, emerge from the same vacuum, and our universe was set on a course of seemingly almost infinite inflation a tiny fraction of a second after the Big Bang. The rub is that when calculating the behavior of cosmic inflation, infinity keeps intruding and destroying any reasonable prediction. To quote Tegmark, “. . .inflation always gives the same useless answer: infinity divided by infinity.”
The reasons for arriving at this useless calculation are technical, but the upshot isn’t: reality comes down to an inconceivable concept. Infinity also intrudes in the fashionable theory of the multiverse, which derives our universe by supposing that it is only one in an infinite, or nearly infinite, number of alternative universes. But for this to be true, there have to be reasonable calculations of the odds for producing our particular universe with all its vast number of stars and galaxies, and these don’t exist. There are infinite reasons for why the Big Bang produced the universe that led to life on Earth and infinite reasons why it might not have happened. This is surely a very unsatisfying situation. Continue reading